# Questions tagged [two-stage-least-squares]

Two-stage least squares (2SLS) is a structural equation modeling technique that is used when the IV is correlated with the DV's errors.

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### 2SLS: does it just rescale the instrument variable?

I am investigating using instrument variables to correct for some known sources of measurement error in my data (measures that reflect mistakes/inconsistencies that we think directly affect our main ...
153 views

### Does an instrumental variable require independence between the instrument and treatment?

An instrumental variable Z is a legitimate instrument for T (the treatment) if the following hold: Z has a causal effect on Y that is fully mediated by T (i.e. no direct effect from Z to Y, and the ...
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### Do first and second stage regressions combined with fixed effects have to follow the same model?

I suspect reverse causality between Y and X1, therefore I'm applying an instrumental variable approach to panel data. My main regression consists of country- and year-fixed effects. Do I have to also ...
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### Instrumental variable with measurement error

I have a question related to measurement error bias and the use of instrumental variables. Assume I have a continuous outcome variable $Y$ which is observed with no error and an endogenous (continuous)...
1 vote
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### Weak instrument but 2nd stage significant

My IV's 1st stage F-stat is 4.7 (considered weak by the rule of thumb). The 2nd-stage regression coefficient is significant. I wonder what is the best way to interpret such observations.
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### Discrepancy in 2SLS Estimation Results

I've been exploring the 2SLS (Two-Stage Least Squares) estimation method to analyze a model involving endogeneity and instrumental variables. To better understand the process, I performed manual ...
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### The magnitude of an two-stages least squares coefficient is always larger than the ordinary least squares coefficient?

I have a hard time wrapping my head around this. I know that in case of measurement errors, the OLS estimate is biased downwards zero. Omitted variables can bias the explanatory variable of interest ...
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### IVs: would this rainfall specification cut it?

I need feedback to check whether rainfall is an appropriate instrumental variable. Before you boo me out, hear what I have to say. There are two countries: A and B. A and B are 2000 miles apart. My ...
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### 2SLS with endogenous variable $X_1$ and interaction terms $X_1 \times X_2$, $X_2$ exogenous

I would like clarification on the correct way to set up the first-stage regression(s) for a hypothetical 2SLS regression. Say we have the following formula: \begin{align} y = x_1 + x_2 + x_1 \...
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### Instrumental variable identifiability in a linear setting in the presence of unobserved confounders

Long story short, I'm seeing in the literature that linear instrumental variables models are identifiable, even in the presence of unobserved confounders. The unobserved confounding aspect befuddles ...
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### When is an instrument too strong in the first stage?

Instrumental variable regression is estimated with ivreg in R. ivreg provides diagnostics with the ...
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### Can a variable be an instrument in the first stage and an exogenous covariate in the second stage of an 2SLS regression?

I have two equations of the form: $y = X\beta + Z\gamma + r\alpha +\epsilon_1$ (1) $r = Z\delta +\epsilon_2$ (2) The basic intuition here is $y$ is total cost data, $X$ is a matrix of variables ...
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### Can I have an interaction-term between the predicted endogenous variable and other exogenous variables in the second stage Modell of a 2SLS?

I have a question regarding 2SLS and interaction-terms between the predicted endogenous variable and a set of exogenous variables (second stage). I want to calculate the effect of an endogenous ...
1 vote
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### Two questions about Interaction-terms in IV-regressions (2SLS) in R

I am doing a 2SLS-model in R with panel data (n=800), where I want to include an interaction-term as Instrumental-Variable in the first-stage model. My first question is: Does that even make sense? ...
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### ECM long-run elasticity with one I(2) variable

I am estimating a 2SLS using a time series simultaneous equation ECM. The purpose is to estimate the price elasticity of electricity demand. Assume that both price and demand are I(1) variables, ...
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### Manually calculate robust standard errors of 2SLS regression

I used the "systemfit" function in R to estimate a 2SLS model as it allows to specify the first and second stage separately which is important for my estimation. I need robust standard ...
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### Should I take logarithm of weights in WLS regressions

I am new here. I have a question regarding the anlaytical weights used in ivreghdfe or reghdfe regressions. People usually take aweights in STATA, my question is how we deal with the weight if the ...
1 vote
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### What's the difference between exogenous and endogenous identifiers?

What's the difference? Exogenous vs. Endogenous identifiers.
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### Are standard errors from a second stage with OLS always underestimated? [duplicate]

I use Stata. I build on Standard errors of a two stage least squares regression, Stata to compute manually the standard errors for my model: I cannot use standard packages (ivreg2 etc.) as the second ...
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### What is the 2SLS bias with a zero first stage in instrument analysis

I am trying to understand the impact in the IV estimate when zero coefficient is obtained in the first stage.
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### Can you use two stage least squares (instruments) on an endogenous categorical variable (Likert scale)?

I have an endogenous categorical variable (exlanatory variable) measured on a Likert scale (from 1-4) and I would like to instrument it via 2sls. I am wondering if this is a theoretically correct ...
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### Is my instrumental variable too noisy?

I have an instrument, that I want to use with IV 2SLS, to predict my endogenous variable. The scatter plot of my instrument against my endogenous variable looks like this. Using Stata's binscatter, I ...
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### 2sls second stage statistically insignificant

i conducted a two stage least square regression. The coefficients of my first stage are statistically significant, but my second stage is not. How can i interpretate this? My F-Statistic of the second ...
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### Prediction of the 1st stage in 2SLS not important?

My question was sparked by the discussion Why is the functional form of the 1st stage in 2SLS not important? I understand that in the first-stage we aim to predict our endogenous variable ($\hat{x}$), ...
1 vote
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### Why not simply use your instrumental variable as your independent variable?

I'm a little confused as to why we need to go through an entire two-stage regression process to capture the effect of our instrumental variable on our independent variable, and then only use this ...
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### Why is ignoring prediction error not a concern in instrumental variables?

In his book, Statistical Rethinking (2nd edition, p. 137), Richard McElreath states that including parameters with unobserved values, such as residuals, and treating them as if they were perfectly ...
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### Interpretation of bias with an endogenous variable

I am running an analysis of impacts of immigration on natives' votes to anti-immigration parties, across municipalities. The concern in this type of analysis is that location decisions of immigrants ...
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### Instrumental Variables: satisfying exclusion criterion with Covariates

I have encountered a situation wherein I am trying to ascertain the causal effect of X on Y through an IV approach in a cross-country panel study, but the exclusion restriction is not entirely valid. ...
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### Identifiability of multivariate instrumental variable model

I'm interested in estimating the effects of $X_1$ and $X_2$ on $Y$ in the directed acyclic graph below. $U_1$ and $U_2$ are unobserved confounders. Based on Definition 7.4.1 on p. 248 of Causality ...
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